Determining order lead time for a supply chain using a probability distribution of order lead time

ABSTRACT

In one embodiment, determining order lead time for a supply chain includes generating probability distribution for expected order lead time options, where each probability distribution for expected order lead time option is associated with a category. A category that corresponds to a supply chain is identified. The supply chain has nodes, including a starting node and an ending node that supplies a customer, and designates a path from the starting node to the ending node. A probability distribution for expected order lead time option associated with the identified category is selected as a probability distribution for expected order lead time for the supply chain. The probability distribution for expected order lead time describes ending node demand for the ending node versus order lead time.

RELATED APPLICATIONS

This application claims benefit under 35 U.S.C. §119(e) of U.S.Provisional Application Ser. No. 60/470,068, entitled “StrategicInventory Optimization,” filed May 12, 2003.

TECHNICAL FIELD

This invention relates generally to the field of supply chain analysisand more specifically to determining order lead time for a supply chainusing a probability distribution for expected order lead time.

BACKGROUND

A supply chain supplies a product to a customer, and may include nodesthat store inventory such as parts needed to produce the product. Aknown technique for maintaining a proper amount of inventory at eachnode may involve setting a reorder point at which inventory isreordered. For example, a node may reorder parts when its inventory isless than twenty units. Known techniques for maintaining a proper amountof inventory at each node, however, may require storage of excessinventory at the nodes and result in additional inventory carryingcosts. It is generally desirable to reduce excess inventory andassociated inventory carrying costs.

SUMMARY OF THE INVENTION

In accordance with the present invention, disadvantages and problemsassociated with previous supply chain analysis techniques may be reducedor eliminated.

According to one embodiment of the present invention, determining orderlead time for a supply chain includes generating probabilitydistribution for expected order lead time options, where eachprobability distribution for expected order lead time option isassociated with a category. A category that corresponds to a supplychain is identified. The supply chain has nodes, including a startingnode and an ending node that supplies a customer, and designates a pathfrom the starting node to the ending node. A probability distributionfor expected order lead time option associated with the identifiedcategory is selected as a probability distribution for expected orderlead time for the supply chain. The probability distribution forexpected order lead time describes ending node demand for the endingnode versus order lead time.

Certain embodiments of the invention may provide one or more technicaladvantages. For example, different probability distribution for expectedorder lead times may be generated for different groups of customers.Generating different probability distribution for expected order leadtimes may allow a user to more efficiently select the probabilitydistribution for expected order lead time for a customer. The user maythen optimize inventory to satisfy the probability distribution forexpected order lead time of the customer.

Certain embodiments of the invention may include none, some, or all ofthe above technical advantages. One or more other technical advantagesmay be readily apparent to one skilled in the art from the figures,descriptions, and claims included herein.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and itsfeatures and advantages, reference is made to the following description,taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram illustrating an example system for optimizinginventory in a supply chain;

FIG. 2 is a flowchart illustrating an example method for optimizinginventory in a supply chain;

FIG. 3 illustrates an example matrix that may be used to generatecriticality groups;

FIG. 4 is a diagram illustrating an example supply chain that receivessupplies from one or more suppliers and provides products to one or morecustomers;

FIG. 5 is a flowchart illustrating an example method for inventoryoptimization;

FIGS. 6A through 6C illustrate example order lead time profiles;

FIG. 7 is a bar graph illustrating example cycle times for nodes of asupply chain;

FIG. 8 is a table with example demand percentages;

FIG. 9 is a diagram illustrating redistributed demand for an examplesupply chain;

FIG. 10 illustrates an example node for which an inventory may becalculated;

FIG. 11 illustrates an example supply chain that includes one nodesupplying another node;

FIG. 12 illustrates an example supply chain that includes one nodesupplying two nodes; and

FIG. 13 illustrates an example supply chain that includes two nodessupplying one node.

DESCRIPTION OF EXAMPLE EMBODIMENTS

FIG. 1 is a block diagram illustrating an example system 10 foroptimizing inventory in a supply chain that supplies products tocustomers in response to customer demand. For example, system 10 mayoptimize target safety stocks or other inventory measures, within aminimum overall target customer service level (CSL), at each node in thesupply chain for each item flowing through the supply chain. Accordingto one embodiment, system 10 may use assumptions to formulate a supplychain model, and evaluate the assumptions with respect to historicalperformance. According to another embodiment, products may be segmentedinto policy groups, such as criticality groups, for example, in order todetermine customer service levels for the products. According to yetanother embodiment, order lead times may be used to redistributecustomer demand to upstream nodes of the supply chain.

According to the illustrated embodiment, system 10 includes a clientsystem 20, a server system 24, and a database 26 coupled as shown inFIG. 1. Client system 20 allows a user to communicate with server system24 to optimize inventory in a supply chain. Server system 24 managesapplications for optimizing inventory in a supply chain. Database 26stores data that may be used by server system 24.

According to the illustrated embodiment, server system 24 includes oneor more processors 30 and one or more engines 32 coupled as shown inFIG. 1. Processors 30 manage the operation of server system 24, and maycomprise any device operable to accept input, process the inputaccording to predefined rules, and produce an output. According to oneembodiment, processors 30 may comprise parallel processors in adistributed processing environment. Server system 24 may operate todecompose an optimization problem into a number of smaller problems tobe handled by a number of processors 30. As an example, server system 24may independently calculate the optimized inventory target for each of anumber of nodes using a different processor 30.

According to the illustrated embodiment, engines 32 includes a demandmanager 33, a simulation engine 34, an analytics engine 36, anoptimization engine 38, and a supply chain planning engine 40. Engines32 may be configured in processors 30 in any suitable manner. As anexample, engines 32 may be located in different processors 30. Asanother example, a backup for an engine 32 and the engine 32 itself maybe located in different processors 30. Demand manager 33 provides demandforecasting, demand planning, other demand management functionality, orany combination of the preceding. Simulation engine 34 simulatesexecution of a supply chain. Simulation engine 34 may be used toevaluate supply chain models. Analytics engine 36 analyzes inventory,demand, and order lead time data. Analytics engine 36 may be used tosegment customers, items, locations, other entities, or any combinationof the preceding into policy groups for different purposes. Optimizationengine 38 optimizes the inventory at the nodes of a supply chain. Demandmay be distributed to upstream nodes according to a demand forecast, andoptimization engine 38 may optimize inventory for the distributeddemand. Supply chain planning engine 40 generates a plan for a supplychain.

Client system 20 and server system 24 may each operate on one or morecomputers and may include appropriate input devices, output devices,mass storage media, processors, memory, or other components forreceiving, processing, storing, and communicating information accordingto the operation of system 10. For example, the present inventioncontemplates the functions of both client system 20 and server system 24being provided using a single computer system, such as a single personalcomputer. As used in this document, the term “computer” refers to anysuitable device operable to accept input, process the input according topredefined rules, and produce output, for example, a personal computer,work station, network computer, wireless telephone, personal digitalassistant, one or more microprocessors within these or other devices, orany other suitable processing device.

Client system 20, server system 24, and database 26 may be integrated orseparated according to particular needs. If any combination of clientsystem 20, server system 24, or database 26 are separated, they may becoupled to each other using a local area network (LAN), a metropolitanarea network (MAN), a wide area network (WAN), a global computer networksuch as the Internet, or any other appropriate wire line, optical,wireless, or other link.

Modifications, additions, or omissions may be made to system 10 withoutdeparting from the scope of the invention. For example, system 10 mayhave more, fewer, or other modules. Moreover, the operations of system10 may be performed by more, fewer, or other modules. For example, theoperations of simulation engine 34 and optimization engine 38 may beperformed by one module, or the operations of optimization engine 38 maybe performed by more than one module. Additionally, functions may beperformed using any suitable logic comprising software, hardware, otherlogic, or any suitable combination of the preceding. As used in thisdocument, “each” refers to each member of a set or each member of asubset of a set.

FIG. 2 is a flowchart illustrating an example method for optimizinginventory in a supply chain. The method may be used to separate thedemand analysis from the supply analysis by redistributing the demand toupstream nodes and then calculating the inventory required to satisfythe redistributed demand. Separating the demand may provide for moreefficient inventory analysis. The method begins at step 48, where asupply chain model is formulated for a supply chain. A supply chainmodel may be used to simulate the flow of items through the supplychain, and may represent one or more constraints of a supply chain. Aconstraint comprises a restriction of the supply chain. The supply chainmodel may have one or more assumptions. An assumption comprises anestimate of one or more parameters of a supply chain model.

The assumptions are evaluated at step 50. The assumptions may beevaluated by simulating the supply chain using the supply chain modeland validating the simulation against historical data describing actualperformance of the supply chain. Historical data describing a first timeperiod may be applied to the supply chain model to generate a predictiondescribing a second time period. For example, given one year of data,the first ten months of data may be used with the supply chain model topredict the last two months of data. The prediction for the second timeperiod may be compared to the historical data describing the second timeperiod in order to evaluate the assumptions of the supply chain model.The assumptions may be adjusted in response to the evaluation.

The inventory is analyzed at step 52. The inventory may be analyzed bysegmenting products into policy groups such as criticality groups. Eachcriticality group may correspond to a particular inventory policy suchas a customer service level. Customer demand and order lead time mayalso be analyzed to determine demand and order lead time means andvariability. The inventory is optimized at step 54 to determine anoptimized inventory for each node of the supply chain. The sensitivityof the optimized inventory may be analyzed by adjusting the assumptionsand checking the sensitivity of the inventory to the adjustment.According to one embodiment, the assumptions may be relaxed in order toreduce the complexity of the optimization.

The optimization may be validated at step 56. During validation, anyassumptions that were relaxed during optimization may be tightened. Aninventory policy may be determined at step 58. According to oneembodiment, a user may decide upon an inventory policy in response tothe validation results. The inventory policy is implemented in thephysical supply chain at step 60.

The inventory performance may be evaluated at step 62 by determiningwhether the inventory performance satisfies inventory performancemeasures. In response to evaluating the inventory performance, themethod may return to step 48 to formulate another supply chain model, tostep 50 to re-evaluate the assumptions, to step 52 to re-analyze theinventory, or to step 58 to determine another inventory policy, or themethod may terminate. According to one embodiment, an actual customerservice level may be measured at a first time period. If the actualcustomer service level fails to satisfy the target customer servicelevel, deviations between actual and assumed input values may bedetermined. The deviations may be determined according to definedworkflows that are consistent and repeatable over successive timeperiods. An input value with a deviation may be identified to be a rootcause of the failure and this information used as feedback for asubsequent time period. During the subsequent time period, the assumedvalue for the identified input may be adjusted and used to calculate areoptimized inventory target. According to the embodiment, the steps ofthe method may be repeated in an iterative closed-loop process that isconsistent and repeatable over successive time periods. The iterativeclosed-loop process may use the assumed values of the inputs as itsinputs and the actual customer service level as its output.

Modifications, additions, or omissions may be made to the method withoutdeparting from the scope of the invention. For example, the step ofevaluating the assumptions may be omitted. Additionally, steps may beperformed in any suitable order without departing from the scope of theinvention. For example, the step of evaluating the assumptions may beperformed after the step of analyzing inventory. Furthermore, althoughthe method is described as optimizing inventory for each node of thesupply chain, the method may be used to optimize inventory for a subsetof one or more nodes of the supply chain.

FIG. 3 illustrates an example matrix M_(i . . . j) 66 that may be usedto generate policy groups such as criticality groups. A policy groupcomprises a set of entities strategically segmented for a particularpurpose. An entity may comprise, for example, a product, a location, ora customer of a supply chain. According to one embodiment, a policygroup may refer to a criticality group for which a service level policyis defined. A service level policy describes the level of service for anentity, and may include a customer service level, a lead time, or otherparameter. As an example, segmentation may classify customers intocriticality groups, where each criticality group has a specifiedcustomer service level. Criticality groups may be used to definedifferent service levels for different customers. According to anotherembodiment, a policy group may refer to a set of entities that exhibitcommon buying behaviors, for example, common order lead time profiles.

According to the illustrated example, matrix M_(i . . . j) 66 is used tosegment products into criticality groups, where each entry, or cell,m_(i . . . j) represents a criticality group with a specific servicelevel policy. Matrix M_(i . . . j) 66 may have any suitable number ofindices i . . . j, where each index represents an attribute of theentities. An attribute comprises a feature of an entity that is relevantto the service level associated with the entity, and may be quantitativeor non-quantitative. Examples of quantitative attributes includeinventory volume, revenue calculated as volume times price, marginvolume calculated as price minus cost, or other attributes. Examples ofnon-quantitative attributes may include product tier or life cycle,number of customers served, or other attributes. According to theillustrated example, index i represents the relative speed with whichitems for the product move through the supply chain, and j representswhether there is a hub agreement with the nodes through which the itemsflow. An index may, however, represent any suitable attribute. As anexample, an index may be used to define target customer service levels,minimum offered lead times, maximum offered lead times, or anycombination of the preceding for each criticality group. Eachcriticality group may represent a unique combination of item, location,and channel.

As used herein, the term “matrix” is meant to encompass any suitablearrangement of attributes in which each attribute associated with thematrix corresponds to at least one index of the matrix and maycorrespond to any number of indexes of the matrix. Such a matrix mayhave any suitable format. As an example, different cells may havedifferent indices. As another example, policy groups corresponding todifferent cells may overlap. Membership to overlapping policy groups maybe resolved by, for example, assigning priorities to the policy groups.An attribute not corresponding to any index of the matrix may beassigned to a default policy group.

FIG. 4 is a diagram illustrating an example supply chain 70 thatreceives supplies from one or more suppliers 80 and provides products toone or more customers 84. Items flow through supply chain 70, and may betransformed or remain the same as they flow through supply chain 70.Items may comprise, for example, parts, supplies, or services that maybe used to generate the products. The products may include none, some,or all of some or all of the items. For example, an item may comprise apart of the product, or an item may comprise a supply that is used tomanufacture the product, but does not become a part of the product.Downstream refers to the direction from suppliers 80 to customers 84,and upstream refers to the direction from customers 84 to suppliers 80.

Supply chain 70 may include any suitable number of nodes 76 and anysuitable number of arcs 78 configured in any suitable manner. Accordingto the illustrated embodiment, supply chain 70 includes nodes 76 andarcs 78. Items from supplier 80 flow to node 76 a, which sends items tonode 76 b. Node 76 b sends items to node 76 c, which sends items tocustomer 84 a and nodes 76 d and 76 e. Nodes 76 d and 76 e provideproducts to customers 84 b and 84 c, respectively.

Node 76 a may comprise one of one or more starting nodes 76 a upstreamfrom one or more ending nodes 76 d-e. Starting nodes 76 a may receiveitems directly from supplier 80 or from an upstream node 76, and endingnodes 76 c-e may send items directly to a customer 84 a-c or to adownstream node 76. A starting node 76 a and an ending node 76 c-e maydefine a path that includes starting node 76 a, ending node 76 c-e, andany intermediate nodes 76 b-c between starting node 76 a and an endingnode 76 c-e.

Although supply chain 70 is illustrated as having five nodes 76 a-e andfour arcs 78 a-d, modifications, additions, or omissions may be made tosupply chain 70 without departing from the scope of the invention. Forexample, supply chain 70 may have more or fewer nodes 76 or arcs 78.Moreover, nodes 76 or arcs 78 may have any suitable configuration. Forexample, node 76 a may supply items to node 76 c, but not to node 76 b.As another example, any node 76 may supply items directly to a customer84.

The products may be delivered to a customer 84 according to an orderlead time for customer 84. An order lead time represents the time periodduring which supply chain 70 may satisfy an order. The order lead timefor customer 84 may be calculated as the time between the time when theorder is finalized and the time when the order is to be provided tocustomer 84. The time when an order is finalized may be different fromthe time when the order was placed, since the order may be modifiedbefore the order is finalized. A finalized order may refer to an orderat any suitable stage of the supply chain process. For example,finalized orders may refer to last changed orders, orders that have beenshipped, orders that are in backlog, other suitable orders, or anycombination of the preceding.

The order lead time for customer 84 may be described using a probabilitydistribution for expected order lead time. A probability distributionfor expected order lead time describes the probability distribution ofdemand relative to order lead time. A probability distribution forexpected order lead time may be calculated from an order lead timeprofile. An order lead time profile describes demand with respect toorder lead time, and may be generated from a demand profile thatdescribes demand with respect to time. The demand may be expressed asunit demand, as a proportion of the demand, or in any other suitablemanner. As an example, an order lead time profile may describe acumulative percentage of the demand with respect to order lead time. Forexample, an order lead time profile may have a y axis representing thecumulative percentage of demand and an x axis representing order leadtime expressed as number of days. An example order lead time profiles isdescribed in more detail with reference to FIG. 6.

Although the probability distribution for expected order lead time maybe calculated from an order lead time profile, the probabilitydistribution may be determined from other suitable types of informationusing any suitable number of parameters. For example, the probabilitydistribution may be determined from the absolute demand volume withrespect to time. As another example, the probability distribution may bedetermined using a fuzzy logic approach. A fuzzy logic approach may, forexample, designate that a certain amount or portion of the demand has aspecific order lead time.

All of the demand typically does not have the same order lead time. Forexample, 70% of the demand may have an order lead time of less than 20days, and 30% of the demand may have an order lead time of 20 days orgreater. If a node 76 can replenish its inventory in time to satisfy aportion of the demand, node 76 does not need to stock the inventory forthat portion of the demand. For example, if node 76 can replenish itsinventory in less than 20 days to satisfy 30% of the demand, node 76does not need to stock inventory for 30% of the demand.

According to one embodiment, the demand initiated by a customer 84 maybe redistributed from a downstream node 76 to one or more upstream nodes76. For example, the demand initiated by customer 84 a, 84 b, or 84 cmay be redistributed from downstream node 76 c, 76 d, or 76 e,respectively, to one or more upstream nodes 76 a-c. Optimization of theredistributed demand may be postponed to upstream nodes 76 a-c.Redistributing demand upstream may serve to optimize supply chain 70.Typically, maintaining items at upstream nodes 76 is less expensive thanmaintaining items at downstream nodes 76. Additionally, more developeditems at downstream nodes 76 are typically more susceptible to marketchanges. A method for optimizing inventory by redistributing demand toupstream nodes 76 is described in more detail with reference to FIG. 5.

According to one embodiment, redistributing the demand upstream involvestaking into account the time it takes for supplies needed at nodes 76 tobe replenished and the reliability of the supply nodes 76. Thereplenishment time may be determined from supply lead times (SLTs).According to the illustrated example, the mean supply lead time(μ_(SLT)) for node 76 a is 20.0 days with a variability (σ_(SLT)) of 6.0days, the mean supply lead time for arc 78 a is 1.5 days with avariability of 0.5 days, the mean supply lead time for node 76 b is 6.0days with a variability of 2.67 days, the mean supply lead time for node76 c is 0.0 days with a variability of 0.00 days, the mean supply leadtime for arc 78 b is 1.0 day with a variability of 0.33 days, and themean supply lead time for arc 78 c is 1.5 days with a variability of 0.5days. Node 76 c may be considered a global distribution node. Thereliability of the supply nodes 76 may be determined from the customerservice levels of nodes 76. According to the illustrated example, thecustomer service level for node 76 a is 80%, and the customer servicelevels for nodes 76 b and 76 c are 96%.

FIG. 5 is a flowchart illustrating an example method for inventoryoptimization. The method begins at step 104, where order lead timeprofiles are created for different categories. Categories may be used toorganize customers, products, locations, other entity, or anycombination of the preceding. For example, customers 84 may becategorized according to features that affect the order lead times ofcustomers 84, such as demand requirements that the customers 84 arerequired to satisfy, expected order lead times for the customer'sindustry, or other features. These features may be identified using alead time history. As another example, product shipment size may be usedto categorize products, or channel efficiency may be used to categorizechannels.

A lead time profile for the supply chain 70 of a specific customer 84 isdetermined at step 106. The specific order lead time profile may bedetermined by identifying the category to which the specific customer 84belongs, and selecting the order lead time profile that corresponds tothe identified category from the order lead time profile options.According to one embodiment, the lead time profile for a specificcustomer 84 may be modified to customize the order lead time profile. Asan example, the order lead time profile may be modified by a user usinga user interface to account for a predicted change in customer demand.The predicted change may result from, for example, item shortages,profit increase, economic downturn, or other economic factor. As anotherexample, the order lead time profile may be modified to account for amaximum offered lead time or a minimum offered lead time. An exampleorder lead time profile is described in more detail with reference toFIG. 6.

Supply chain 70 is divided into order lead time segments (OLTSs) at step110. An order lead time segment represents a portion of the path ofsupply chain 70 that may be used to distribute order lead times anddemand upstream. Cycle times may be used to establish the order leadtime segments. A cycle time for a node 76 or arc 78 represents thedifference between the time when an item arrives at the node 76 or arc78 and the time when the item leaves the node 76 or arc 78. For example,the cycle time for a node 76 may include a manufacturing, production,processing, or other cycle time. The cycle time for an arc 78 mayinclude a distribution, transportation, or other cycle time. Acumulative cycle time for a node 76 represents the difference betweenthe time when an item arrives at the node 76 and the time when the endproduct is delivered to customer 84. A cumulative cycle time may includethe sum of one or more individual cycle times involved, for example, thecycle times for one or more nodes 76 and one or more arcs 78 involved.As an example, an order lead time segment may represent the differencebetween the cumulative cycle times for a first node 76 and an adjacentsecond node 76. Examples of order lead time segments are described withreference to FIG. 7.

The supply lead time (SLT) for each order lead time segment iscalculated at step 112. According to one embodiment, the supply leadtime SLT for an order lead time segment may be calculated according toSLT=μ+xσ for y % certainty. Values x and y may be determined accordingto standard confidence levels. For example, x=3 for y=99. According tothe example supply chain 70 of FIG. 4, for 99% certainty, the supplylead time for arc 78 c is 1.5+3(0.5)=3.0 days. Similarly, for 99%certainty, the supply lead time for arc 78 b is 2.0 days, and the supplylead time for arc 78 a is 3.0 days. The supply lead time, however, maybe calculated according to any suitable formula having any suitableparameters. For example, the supply lead time SLT may be calculatedaccording to SLT=p₁+p₂, where p₁ represents a minimum delay, and p₂represents an expected additional delay. Moreover, the supply lead timesmay have any suitable relationship with each other. For example, atleast two of the supply lead times may overlap. Furthermore, the supplylead times may be adjusted in any suitable manner. For example, a oneday padding may be added to one or more supply lead times.

Demand is redistributed to upstream order lead time segments at step 114in order to postpone inventory calculation to upstream nodes 76. Demandmay be redistributed by estimating demand percentages for the order leadtime segments. A demand percentage for an order lead time segmentrepresents the percentage of the demand that needs to be satisfiedduring the order lead time segment in order to satisfy the customerdemand within the constraints of the order lead time profile. An exampleof calculating demand percentages is described with reference to FIGS. 8and 9.

Inventory that satisfies the demand percentages is established at nodes76 at step 120. By calculating a demand percentage for each order leadtime segment, the inventory for the redistributed demand may bedetermined by postponing inventory calculation and individuallycalculating the inventory at each node 76. The inventory may bedetermined by calculating the inventory required at ending nodes 76 (forexample, nodes 76 d and 76 e) to satisfy the demand percentage of endingnodes 76. The calculated inventory generates a demand for a firstupstream node 76 (for example, node 76 c). The inventory at the firstupstream node 76 is determined to generate a demand for a secondupstream node 76 (for example, node 76 c), and so on. Inventory neededto satisfy the redistributed demand may be combined with inventoryneeded without regard to the redistributed demand in order to determinethe total demand needed at a node 76. A method for establishing theinventory is described in more detail with reference to FIGS. 10 through13.

Modifications, additions, or omissions may be made to the method withoutdeparting from the scope of the invention. For example, order lead timeprofiles need not be created for different categories at step 104.Instead, an order lead time profile for the specific customer 84 maysimply be retrieved. Additionally, steps may be performed in anysuitable order without departing from the scope of the invention.

FIGS. 6A through 6C illustrate example order lead time profiles. Anorder lead time profile describes a demand corresponding to a node 76such as an ending node 76 (for example, node 76 d or 76 e). For example,an order lead time profile may describe demand associated with customer84 a of FIG. 4. The customer demand is placed on ending node 76 d tofulfill. In the illustrated embodiment, the order lead time profile isunconstrained (that is, assumes unlimited supply). Although the exampleorder lead time profiles are illustrated as graphs, the information ofthe order lead time profiles may be presented in any suitable manner,for example, in a table.

FIG. 6A illustrates an example order lead time profile. According to theillustrated embodiment, a y axis 152 represents the cumulativepercentage of demand volume, and an x axis 154 represents the order leadtime expressed in days. According to one embodiment, a curve 160represents an example of an order lead time profile that describes thecumulative percentage of demand volume having a certain order lead time.Accordingly, a point (x, y) of curve 160 represents that cumulativepercentage y of the demand volume has an order lead time of x days. Forexample, a point P indicates that 33% of the demand volume has an orderlead demand time of less than 3 days, a point Q indicates that 90% ofthe demand volume has an order lead time of 30 days, and a point Rindicates that 100% of the demand volume has an order lead time of lessthan 60 days.

In one embodiment, order lead time profiles may be generated fordifferent group levels, for example, for all orders, all items, alllocations, or other group level. Generating order lead time profiles atthe group level may result in generating fewer profiles, which may beeasier to manage. Moreover, a user may be able to select a profile basedupon the group level of interest. In another embodiment, multiple orderlead time profiles may be generated for a group level. For example, anorder lead time profile may be generated for each item. Generatingmultiple order lead time profiles may allow for fine-tuned demandmonitoring. For example, where an order lead time profile is generatedfor each item, the order lead time profile for each item may beautomatically monitored for changes that may impact optimal inventorytarget levels.

FIGS. 6B and 6C illustrate example order lead time profiles customizedto account for maximum and minimum offered lead times, respectively. Anorder lead time profile may be customized using system 10. Pastperformance is not necessarily a good indicator of future performance.System 10 gives the user an opportunity to override or modify an orderlead time profile using client system 10. An order lead time profile maybe customized to account for maximum and minimum offered lead times. Auser may want to impose a minimum offered lead time on an order leadtime profile. An order lead time profile may be modified to reflect aminimum offered lead time by shifting the demand that is less than theminimum offered lead time to the minimum offered lead time. Moreover, auser may want to impose a maximum offered lead time on an order leadtime profile. An order lead time profile may be modified to reflect amaximum offered lead time by shifting the demand that is greater thanthe maximum offered lead time to the maximum offered lead time.

In the illustrated example, curve 160 has been modified to take intoaccount a minimum offered lead time and a maximum offered lead time toyield curves 162 and 164, respectively. Curve 162 takes into account aminimum offered lead time of 10 days, and curve 164 takes into account amaximum offered lead time of 40 days. A curve 160 of an order lead timeprofile may be modified in any other suitable manner to take intoaccount any other suitable feature. For example, order lead timeprofiles over time may be examined using a waterfall analysis todetermine trends. An order lead time profile may be adjusted to fit thetrends. As another example, an order lead time profile may be adjustedto provide a more conservative estimate or a less conservative estimate.

FIG. 7 is a bar graph 200 illustrating example cycle times for nodes 76of supply chain 70. Bar graph 200 has a y axis that represents thecumulative cycle time of a node 76, and an x axis that represents thenode 76. The cumulative cycle time represents the difference between thetime when an item reaches node 76 and the time when the end product isdelivered to customer 84. According to bar graph 200, node 76 a has acumulative cycle time of 60 days, node 76 b has a cumulative cycle timeof 30 days, node 76 c has a cumulative time of 3 days, and nodes 76 dand 76 e each have a cumulative cycle time of 0 days.

The cumulative cycle times may be used to define order lead timesegments representing a difference between cumulative cycle times.According to one embodiment, an order lead time segment may representthe difference between cumulative cycle times for successive nodes 76.According to the illustrated embodiment, order lead time segment 1represents less than or equal to 3 days, order lead time segment 2represents greater than 3 and less than or equal to 30 days, order leadtime segment 3 represents greater than 30 and less than or equal to 60days, and order lead time segment 4 represents greater than 60 days.Order lead time segments may, however, be defined in any suitablemanner.

FIG. 8 is a table 220 with example demand percentages. A demandpercentage represents the percentage of the demand that needs to besatisfied during an order lead time segment in order to satisfy an orderlead time profile.

According to the illustrated example, table 220 illustrates how tocalculate demand percentages for order lead time segments 1 through 4 ofFIG. 7 using order lead time profile curve 160 of FIG. 6. Table 220shows the range of each segment determined as described previously withreference to FIG. 7. The endpoints of each segment correspond to pointsof curve 160 of FIG. 6. For example, the three day endpoint correspondsto point P, the 30 day endpoint corresponds to point Q, and the 60 dayendpoint corresponds to point R.

Each point of curve 160 indicates a cumulative percentage of the demandthat corresponds to the number of days. For example, point P indicatesthat 33% corresponds to 3 days, point Q indicates that 90% correspondsto 30 days, and point R indicates that 100% corresponds to 60 days. Thedifference in the demand corresponding to the endpoints of the orderlead time segment yields the demand percentage. Accordingly, order leadtime segment 1 has a demand percentage of 33%−0%=33%, order lead timesegment 2 has a demand percentage of 90%−33%=57%, order lead timesegment 3 has a demand percentage of 100%−90%=10%, and order lead timesegment 4 has a demand difference of 100%−100%=0%.

FIG. 9 is a diagram illustrating an example redistributed demand for anexample supply chain 70. According to the illustrated example, thedemand may be redistributed according to table 220 of FIG. 8. The demandpercentage for OLTS1 is 33%, for OLTS2 is 57%, for OLTS3 is 10%, and forOLTS4 is 0%.

FIGS. 10 through 13 illustrate example procedures for calculatinginventory for the nodes 76 of a supply chain 70, given the demand,supply lead times, and customer service level for the nodes 76. If thedemand for a supply chain 70 is redistributed to upstream nodes 76, theinventory for the nodes 76 may be calculated for the distributed demand,which may be calculated using the demand percentages of the nodes 76.The inventory for the distributed demand may then be combined with theinventory for customer demand to obtain the total inventory for nodes76.

FIG. 10 illustrates an example supply chain portion 240 with a node 76(node 1) for which an inventory may be calculated. According to oneembodiment, the customer service level CSL for node 1 may be expressedaccording to EquationCSL=1−EBO/μ _(d)  (1)where EBO represents the expected back order of node 1 and μ_(d)represents the mean lead time demand. Expected back order representsinsufficient inventory of node 76 to meet demand at node 76. The leadtime demand describes the demand for a lead time segment. Expected backorder EBO may be calculated according to Equation (2):

$\begin{matrix}{{EBO} = {\int_{s}^{\infty}{( {x - {fs}} ){p(x)}\ {\mathbb{d}x}}}} & (2)\end{matrix}$where p(x) represents the probability density function around the meanlead time demand, s represents a reorder point, and f represents apartial fulfillment factor. If partial fills are not allowed, then f=0and the term drops out. The demand distribution may typically beconsidered a Normal distribution for relatively fast moving items interms of demand over lead time, a Gamma distribution for items moving ata relatively intermediate speed in terms of demand over lead time, or aPoisson distribution for relatively slow moving items in terms of demandover lead time. The distribution may be selected by a user or may be adefault selection. The mean lead time demand may be calculated accordingto Equation (3):

$\begin{matrix}{µ_{d} = {\int_{- \infty}^{\infty}{{{xp}(x)}\ {\mathbb{d}x}}}} & (3)\end{matrix}$

According to one example, for a fixed supply lead time (SLT), theinventory of node 1 may be calculated to propagate demand given the meanlead time demand μ_(d) of demand d, the standard deviation of lead timedemand σ_(d) of demand d (where standard deviation is used as oneexample measure of variability), and the customer service level CSL.According to the illustrated example, mean lead time demand μ_(d) is1000 units with a variability σ_(d) of 10 units, and node 1 has acustomer service level CSL of 96%. The inventory needed to cover meanlead time demand μ_(d) with x customer service level may be calculatedas μ_(d)+xσ_(d), where x corresponds to y according to standardconfidence levels. For example, node 1 needs μ_(d)+2σ_(d) to cover thedemand 96% of the time. In the illustrated example, the inventory neededat node 1 is μ_(d)+2σ_(d)=1020 Units. To satisfy the remaining demand,there is an expected back order EBO=μ_(d)×(1−CSL). In the illustratedexample, the expected back order EBO=μ_(d)×(1−CSL)=40 units. Inventorymay be calculated for a number m of time periods by multiplying theinventory units by m.

According to one embodiment, demand may be propagated to determine themean lead time demand and variability at each node 76. Then, inventorymay be calculated at individual nodes 76 using known techniques, whichmay simplify inventory optimization. In other words, a complicatedmulti-echelon supply chain problem may be reduced to a series of simplersingle echelon supply chain problems.

FIG. 11 illustrates an example supply chain portion 250 that includesone node 76 (node 1) supplying another node 76 (node 2). According tothe illustrated embodiment, node 1 has a demand d over the lead timewith a demand variability of σ_(d). Node 1 has a customer service levelCSL1 and a supply lead time SLT1 with a supply lead time variability ofσ_(SLT1), and node 2 has a customer service level CSL2 and a supply leadtime SLT2 with a supply lead time variability of σ_(SLT2).

According to one embodiment, the supply lead time for node 1 may becalculated according to Equation (4):CSL2*SLT1+(1−CSL2)*(SLT1+SLT2)  (4)and the supply lead time variability may be calculated according toEquation (5):CSL2*σ_(SLT1)+(1−CSL2)*(σ_(SLT)1+σ_(SLT2))  (5)

FIG. 12 illustrates an example supply chain portion 270 that includesone node 76 (node 3) supplying two nodes 76 (nodes 1 and 2). Node 1 hasa demand d1 with a demand variability of σ_(d1) and a customer servicelevel CSL1. Node 2 has a demand d2 with a demand variability of σ_(d2)and a customer service level CSL2. Node 1 has a supply lead time SLT1with a supply lead time variability σ_(SLT1), and node 2 has a supplylead time SLT2 with a supply lead time variability σ_(SLT2). Node 3 hasa supply lead time SLT3 with a supply lead time variability of σ_(SLT3).

According to one embodiment, supply chain portion 270 represents asingle distribution center that supports multiple distribution centersor a single die that makes multiple products. The demand at node 3 maybe given by d1+d2 with a demand variability given by Equation (6):√{square root over (σ_(d1) ²+σ_(d2) ²+cov(σ_(d1),σ_(d2)))}  (6)In a simple case, the covariance may be assumed to equal zero. Thesupply lead time and supply lead time variability of node 1 may becalculated according to Equations (4) and (5), respectively. Accordingto another embodiment, supply chain portion 270 may represent a node 76with multiple demand streams. According to this embodiment, supply chainportion 270 may represent multiple demand streams if supply lead timeSLT1=0, supply lead time variability σ_(SLT1)=0, supply lead timeSLT2=0, and supply lead time variable σ_(SLT2)=0. According to oneembodiment, demand of nodes 1 and 2 may be aggregated at node 3. Thedemand of nodes 1 and 2 may be pooled in order to calculate the demandof node 3.

FIG. 13 illustrates an example supply chain portion 280 that includestwo nodes 76 (nodes 2 and 3) supplying one node 76 (node 1). Node 1 hasa customer service level CSL1 and a demand d1 with a demand variabilityσ_(d1). Node 2 has a customer service level CSL2 and node 3 has acustomer service level CSL3. Node 1 has a supply lead time SLT2 with asupply lead time variability σ_(SLT2) from node 2, and a supply leadtime SLT3 with a supply lead time variability σ_(SLT3) from node 3.

According to one embodiment, supply chain portion 280 may representproduct substitutions, alternative components, or alternate distributionroutes. According to the embodiment, supply chain portion 280 representsnode 1 receiving supplies from alternate sources nodes 2 and 3. Node 1receives a portion θ, where 0<θ<1, from node 2 and a portion 1-θ fromnode 3. According to this embodiment, the lead time for node 1 may begiven by Equation (7):θ*SLT1+(1−θ)*SLT3  (7)with a lead time variability given by Equation (8):θ*σ_(SLT1)+(1−θ)*σ_(SLT2)  (8)

According to another embodiment, supply chain portion 280 may representnode 1 requiring supplies from both nodes 2 and 3 to create or assemblea product. According to this embodiment, this representation of portionθ is not used since node 1 requires items from both nodes 2 and 3.According to the embodiment, the lead time at node 1 may be given byEquation (9):Max(SLT2,SLT3)  (9)with a lead time variability given by Equation (10):⅓[Max(SLT2+xσ_(SLT2),SLT3+Xσ_(SLT3))−Max(SLT2,SLT3)]  (10)where x may be determined according to standard confidence levels. Forexample, x=3 for a 99% confidence level.

To summarize, FIGS. 10 through 13 illustrate example procedures forcalculating inventory for the nodes 76 of a supply chain 70. Theinventory may be calculated given the demand, supply lead times, andcustomer service level for the node 76. If the demand for a supply chain70 is redistributed to upstream node 76, the inventory for the nodes 76may be calculated for the redistributed demand, which may be calculatedusing the demand percentages of the nodes 76. Inventory needed tosatisfy the redistributed demand may be combined with inventory neededwithout regard to the redistributed demand in order to determine thetotal demand needed at a node 76.

Certain embodiments of the invention may provide one or more technicaladvantages. For example, demand may be redistributed from an ending nodeto upstream nodes of a supply chain according to a probabilitydistribution for expected order lead time. Redistributing the demand toupstream nodes may allow for optimizing inventory at individual nodes,which may simplify the optimization. Inventory for the supply chain maybe optimized for the redistributed demand. Optimizing inventory forredistributed demand may decrease the need to stock inventory atdownstream nodes, which may minimize cost. Inventory may be optimizedwith respect to a probability distribution for expected order lead timefor a customer. Taking into account the order lead time may improvecontinued performance, which may lead to increased market share.

Although an embodiment of the invention and its advantages are describedin detail, a person skilled in the art could make various alterations,additions, and omissions without departing from the spirit and scope ofthe present invention as defined by the appended claims.

1. A computer-implemented method of determining a probabilitydistribution to represent order lead time, comprising: generating, usinga computer, a plurality of probability distributions of order lead timeoptions, each probability distribution of order lead time optionassociated with one of a plurality of categories; identifying, using thecomputer, a category that corresponds to a supply chain comprising aplurality of nodes, the plurality of nodes comprising a starting nodeand an ending node that supplies a customer, the supply chaindesignating a path from the starting node to the ending node; dividing,using the computer, the path into a plurality of order lead timesegments; selecting, using the computer, a probability distribution oforder lead time option associated with the identified category as aprobability distribution of order lead time of the supply chain, theprobability distribution of order lead time describing order lead timeat an ending node demand of the ending node; and determining a demandpercentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of ending node demand associated with an orderlead time segment.
 2. The method of claim 1, further comprising:associating the plurality of order lead time segments with theprobability distribution of order lead time, each order lead timesegment being associated with a corresponding order lead time range ofthe probability distribution of order lead time and wherein each demandpercentage further describing a percentage of a total ending node demandassociated with the corresponding order lead time segment.
 3. The methodof claim 1, further comprising: determining a demand percentage thatcorresponds with each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of a total ending node demand associated withthe corresponding order lead time segment; and calculating an inventoryat each node of the plurality of nodes according to the demandpercentages of the plurality of nodes.
 4. The method of claim 1, furthercomprising: establishing a minimum offered lead time; and modifying theprobability distribution of order lead time to reflect the minimumoffered lead time.
 5. The method of claim 1, further comprising:establishing a minimum offered lead time; identifying a most upstreamstocking location in the supply chain such that the cumulative lead timefrom the stocking location to the ending node is less than the minimumoffered lead time; computing the expected percentage of demand at theending node, using the order lead time distribution for which order leadtime will be greater than the minimum offered lead time; decrementingthe demand at the ending node by this computed percentage; andcalculating a safety stock at the ending node using the decrementeddemand.
 6. The method of claim 1, further comprising: establishing amaximum offered lead time; and modifying the probability distribution oforder lead time to reflect the maximum offered lead time.
 7. The methodof claim 1, further comprising: establishing a maximum offered leadtime; identifying a portion of ending node demand corresponding to anorder lead time range greater than the maximum offered lead time; andshifting the portion of ending node demand to the maximum offered leadtime in order to modify the probability distribution of order lead timeto reflect the maximum offered lead time.
 8. The method of claim 1,further comprising: establishing a predicted change of ending nodedemand; and modifying the probability distribution of order lead time toreflect the predicted change of ending node demand.
 9. The method ofclaim 1, further comprising generating the probability distribution oforder lead time from an order lead time profile.
 10. The method of claim1, wherein the plurality of categories categorize at least one of aplurality of customers, a plurality of products, a plurality oflocations, and any combination of the preceding.
 11. A system ofdetermining a probability distribution to represent order lead time,comprising: a database configured to store a plurality of probabilitydistributions of order lead time options, each probability distributionof order lead time option associated with one of a plurality ofcategories; and a computer system coupled with the database andconfigured to: identify a category that corresponds to a supply chaincomprising a plurality of nodes, the plurality of nodes comprising astarting node and an ending node that supplies a customer, the supplychain designating a path from the starting node to the ending node;divide the path into a plurality of order lead time segments; select aprobability distribution of order lead time option associated with theidentified category as a probability distribution of order lead time ofthe supply chain, the probability distribution of order lead timedescribing ending node demand of the ending node versus order lead time;and determine a demand percentage of each order lead time segment inaccordance with the probability distribution of order lead time, eachdemand percentage describing a percentage of ending node demandassociated with an order lead time segment.
 12. The system of claim 11,the computer system further configured to: associate the plurality oforder lead time segments with the probability of order lead time, eachorder lead time segment being associated with a corresponding order leadtime range of the probability distribution of order lead time andwherein each demand percentage further describing a percentage of atotal ending node demand associated with the corresponding order leadtime segment.
 13. The system of claim 11, the computer system furtherconfigured to: determine a demand percentage of each order lead timesegment in accordance with the probability distribution of order leadtime, each demand percentage describing a percentage of a total endingnode demand associated with the corresponding order lead time segment;and calculate an inventory at each node of the plurality of nodesaccording to the demand percentages of the plurality of nodes.
 14. Thesystem of claim 11, the computer system further configured to: establisha minimum offered lead time; and modify the probability distribution oforder lead time to reflect the minimum offered lead time.
 15. The systemof claim 11, the computer system further configured to: establish aminimum offered lead time; identify a portion of ending node demandcorresponding to an order lead time range less than the minimum offeredlead time; and shift the portion of ending node demand to the minimumoffered lead time in order to modify the probability distribution oforder lead time to reflect the minimum offered lead time.
 16. The systemof claim 11, the computer system further configured to: establish amaximum offered lead time; and modify the probability distribution oforder lead time to reflect the maximum offered lead time.
 17. The systemof claim 11, the computer system further configured to: establish amaximum offered lead time; identify a portion of ending node demandcorresponding to an order lead time range greater than the maximumoffered lead time; and shift the portion of ending node demand to themaximum offered lead time in order to modify the probabilitydistribution of order lead time to reflect the maximum offered leadtime.
 18. The system of claim 11, the computer system further configuredto: establish a predicted change of ending node demand; and modify theprobability distribution of order lead time to reflect the predictedchange of ending node demand.
 19. The system of claim 11, the computersystem further configured to generate the probability distribution oforder lead time from an order lead time profile.
 20. The system of claim11, wherein the plurality of categories categorize at least one of aplurality of customers, a plurality of products, a plurality oflocations, and any combination of the preceding.
 21. A non-transitorycomputer-readable medium embodied with software for determining aprobability distribution to represent order lead time, the software whenexecuted using a computer is configured to: generate a plurality ofprobability distributions of order lead time options, each probabilitydistribution of order lead time option associated with one of aplurality of categories; identify a category that corresponds to asupply chain comprising a plurality of nodes, the plurality of nodescomprising a starting node and an ending node that supplies a customer,the supply chain designating a path from the starting node to the endingnode; divide the path into a plurality of order lead time segments;select a probability distribution of order lead time option associatedwith the identified category as a probability distribution of order leadtime of the supply chain, the probability distribution of order leadtime describing ending node demand of the ending node versus order leadtime; and determine a demand percentage of each order lead time segmentin accordance with the probability distribution of order lead time, eachdemand percentage describing a percentage of ending node demandassociated with an order lead time segment.
 22. The computer-readablemedium of claim 21, further configured to: associate the plurality oforder lead time segments with the probability distribution of order leadtime, each order lead time segment being associated with a correspondingorder lead time range of the probability distribution of order lead timeand wherein each demand percentage further describing a percentage of atotal ending node demand associated with the corresponding order leadtime segment.
 23. The computer-readable medium of claim 21, furtherconfigured to: determine a demand percentage of each order lead timesegment in accordance with the probability distribution of order leadtime, each demand percentage describing a percentage of a total endingnode demand associated with the corresponding order lead time segment;and calculate an inventory at each node of the plurality of nodesaccording to the demand percentages of the plurality of nodes.
 24. Thecomputer-readable medium of claim 21, further configured to: establish aminimum offered lead time; and modify the probability distribution oforder lead time to reflect the minimum offered lead time.
 25. Thecomputer-readable medium of claim 17, further configured to: establish aminimum offered lead time; identify a portion of ending node demandcorresponding to an order lead time range less than the minimum offeredlead time; and shift the portion of ending node demand to the minimumoffered lead time in order to modify the probability distribution oforder lead time to reflect the minimum offered lead time.
 26. Thecomputer-readable medium of claim 21, further configured to: establish amaximum offered lead time; and modify the probability distribution oforder lead time to reflect the maximum offered lead time.
 27. Thecomputer-readable medium of claim 21, further configured to: establish amaximum offered lead time; identify a portion of ending node demandcorresponding to an order lead time range greater than the maximumoffered lead time; and shift the portion of ending node demand to themaximum offered lead time in order to modify the probabilitydistribution of order lead time to reflect the maximum offered leadtime.
 28. The computer-readable medium of claim 21, further configuredto: establish a predicted change of ending node demand; and modify theprobability distribution of order lead time to reflect the predictedchange of ending node demand.
 29. The computer-readable medium of claim21, further configured to generate the probability distribution of orderlead time from an order lead time profile.
 30. The computer-readablemedium of claim 21, wherein the plurality of categories categorize atleast one of a plurality of customers, a plurality of products, aplurality of locations, and any combination of the preceding.
 31. Asystem of determining a probability distribution to represent order leadtime, comprising: means for generating a plurality of probabilitydistributions of order lead time options, each probability distributionof order lead time option associated with one of a plurality ofcategories; means for identifying a category that corresponds to asupply chain comprising a plurality of nodes, the plurality of nodescomprising a starting node and an ending node that supplies a customer,the supply chain designating a path from the starting node to the endingnode; and means for selecting a probability distribution of order leadtime option associated with the identified category as a probabilitydistribution of order lead time of the supply chain, the probabilitydistribution of order lead time describing ending node demand of theending node versus order lead time; and means for determining a demandpercentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of ending node demand associated with an orderlead time segment.
 32. A method of determining a probabilitydistribution to represent order lead time, comprising: generating aplurality of probability distributions of order lead time options, eachprobability distribution of order lead time option associated with oneof a plurality of categories; identifying a category that corresponds toa supply chain comprising a plurality of nodes, the plurality of nodescomprising a starting node and an ending node that supplies a customer,the supply chain designating a path from the starting node to the endingnode; selecting a probability distribution of order lead time optionassociated with the identified category as a probability distribution oforder lead time of the supply chain, the probability distribution oforder lead time describing ending node demand of the ending node versusorder lead time; establishing a minimum offered lead time; identifying afirst portion of ending node demand corresponding to an order lead timerange less than the minimum offered lead time; shifting the firstportion of ending node demand to the minimum offered lead time in orderto modify the probability distribution of order lead time to reflect theminimum offered lead time; establishing a maximum offered lead time;identifying a second portion of ending node demand corresponding to anorder lead time range greater than the maximum offered lead time;shifting the second portion of ending node demand to the maximum offeredlead time in order to modify the probability distribution of order leadtime to reflect the maximum offered lead time; establishing a predictedchange of ending node demand; modifying the probability distribution oforder lead time to reflect the predicted change of ending node demand;dividing the path into a plurality of order lead time segments;associating the plurality of order lead time segments with theprobability distribution of order lead time, each order lead timesegment being associated with a corresponding order lead time range ofthe probability distribution of order lead time; determining a demandpercentage of each order lead time segment in accordance with theprobability distribution of order lead time, each demand percentagedescribing a percentage of a total ending node demand associated withthe corresponding order lead time segment; and calculating an inventoryat each node of the plurality of nodes according to the demandpercentages of the plurality of nodes.